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The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics, and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.
Elementary Calculus: An Infinitesimal Approach; Nonstandard calculus; Infinitesimal; Archimedes' use of infinitesimals; For further developments: see list of real analysis topics, list of complex analysis topics, list of multivariable calculus topics
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of contemporary mathematics education . Calculus has widespread applications in science , economics , and engineering and can solve many problems for which algebra alone is insufficient.
It would be a few decades later that Newton and Leibniz independently developed infinitesimal calculus, which grew, with the stimulus of applied work that continued through the 18th century, into analysis topics such as the calculus of variations, ordinary and partial differential equations, Fourier analysis, and generating functions.
Precalculus prepares students for calculus somewhat differently from the way that pre-algebra prepares students for algebra. While pre-algebra often has extensive coverage of basic algebraic concepts, precalculus courses might see only small amounts of calculus concepts, if at all, and often involves covering algebraic topics that might not have been given attention in earlier algebra courses.
Calculus of variations is concerned with variations of functionals, which are small changes in the functional's value due to small changes in the function that is its argument. The first variation [ l ] is defined as the linear part of the change in the functional, and the second variation [ m ] is defined as the quadratic part.